A cannonball is launched from ground level. The angle of launch can be changed. For any target position, what values can the launch angle have in order for the ball to hit the target?

A cannonball is launched from ground level. The angle of launch can be changed. For any particular launch angle, how can you calculate the maximum height of the ball, the time to reach that height, ..

A cannonball is launched from a cannon on a cliff. What must the launch velocity be for the ball to hit the moving target? How does this depend on the launch angle?

The view is looking down on an air hockey table. A puck initially moving at constant velocity receives a momentary push in the +y direction at x = -2 as shown in each of the animations (..

A satellite moves at constant velocity when, at x = -2, its thrusters are suddenly engaged, producing a constant force perpendicular to its original motion. Which animation correctly depicts the satellite's motion after the thrusters are ..

Two blocks are connected by a massless, unstretchable string which passes over a frictionless, massless pulley. The pulley is supported from above. When the blocks are released, the system of the two blocks accelerates. What ..

A car and its unseatbelted crash test dummy accelerates uniformly from rest toward an immovable wall. The car bounces off the wall and then decelerates uniformly to a stop.
Click Show Graph to display a ..

Two cars of equal mass and initial velocity to the right collide with a wall. One car is stopped in the collision and the other bounces off the wall with a velocity of smaller magnitude ..

Two objects collide and rebound from each other. The momentum vector of each object as well as the sum of the momentum vectors is displayed. The lengths of the vectors are drawn to the same ..

Two objects collide and stick together. The momentum vector of each object as well as the sum of the momentum vectors is displayed. The lengths of the vectors are drawn to the same scale.
Unphysical ..

Two objects collide and stick together. The momentum vector of each object as well as the sum of the momentum vectors is displayed. The lengths of the vectors are drawn to the same scale.
Unphysical ..

Two objects collide. The momentum vector of each object as well as the sum of the momentum vectors is displayed. The lengths of the vectors are drawn relative to the magnitude of the momentum. The ..

Two gliders collide in an elastic collision. The center of mass of the system of gliders is shown as a black dot. Play the animation. The animation will stop at the beginning of the collision. ..

A green ball makes a glancing elastic collision with an initially stationary red ball. The balls have equal mass. The paths of the balls after the collision are perpendicular. The vectors shown represent momenta.

Two gliders collide in an elastic collision. The x-coordinate of the center of mass of the system of gliders is shown as a black dot. Play the animation. Click Show Graph. The velocities of the ..

Determine the center of mass velocity for this elastic collision. Why is the center of mass velocity the same before and after the collision? Look at the velocity vs. time graphs. If you added a ..

This is a multiple-choice problem. Enter each of the numbers 1 to 4 in the Choice box. Reset after entering a number. Each choice shows a different version of the electric forces on the positive green charge ..

If the green charge is +1.0 uc (microcoulomb), what are the magnitude and direction of the net electric force on the green charge? Note that all the charges are positive.

Two charges (red and blue) are fixed in position on the x-axis. The green vector represents the net electric force on the positive green charge due to the red and blue charges. At what position ..

Two charged objects (red and blue) are fixed in position on the x-axis. When the animation is started, a small green charged object is pushed back and forth between the red and blue objects. (If ..

Two charged objects (red and blue) are fixed in position on the x-axis. When the animation is started, a small green charged object is pushed back and forth between the red and blue objects. (If ..

When you play the animation, the block oscillates horizontally about the origin on a frictionless table. The origin is in the center and the direction of +x is to the right. The oscillation is the ..

A block is suspended from a fixed support by a rubber band. When held in place by the green stick, the rubber band is completely relaxed. When the green stick is pulled away, the block ..

A ball is suspended by strong wires from two posts. The tension forces and weight are shown. Step through the animation using the >> button to see how the forces change for different vertical positions of ..

A ball is suspended by strong wires from two posts. The tension forces and weight are shown. Step through the animation using the >> button to see how the forces change for different horizontal positions of ..

A red box slides down a wall. The box is in motion at t = 0. A constant force (for example, from a hand) is applied on the box to the right. The grid spacing is 1 meter. ..

A red box slides down a wall. The forces on the box are shown. Try changing the parameters (mass of box, coefficient fo kinetic friction, applied force) to see how that affects the force vectors.

A satellite orbits the Earth in a circular orbit. The ratio of the radius of the satellite's orbit to the radius of the Earth is given. The red dot represents an apple falling near the ..

Two satellites orbit Planet Q in circular orbits. The ratios of the orbital radii and of the masses of the satellites are given. The vectors represent the gravitational accelerations and orbital velocities of the satellites.

The space shuttle orbits the Earth. The ratio of the shuttle's orbital radius to the Earth is given.
The view is looking down on a pole. The white line represents a meridian. Hence, it rotates ..

The green satellite orbits the Earth in a geostationary orbit. This means that the satellite orbits in the Earth's equatorial plane and always remains above the same point on the Earth. The rotation of the ..

Two blocks initially rest next to each other on a frictionless surface. (The view is looking down on the surface.) At t = 0, an identical push is applied directly to each block. The push on each ..

Two blocks rest next to each other on a frictionless surface. At t = 0, a push (by a hand for example) is applied directly to the green block. The push remains constant as the two blocks ..

Two blocks rest next to each other on a frictionless surface. At t = 0, a push (by a hand for example) is applied directly to the red block. The push remains constant as the two blocks ..

A pendulum is released from rest and oscillates in a vertical plane. For which positions (A, B, C) is the tangential acceleration 0? maximum? centripetal acceleration 0? maximum?

A pendulum bob is released from rest and oscillates in a vertical plane. For the system of Earth and bob, match the energy bars with the energy terms that they represent.

A pendulum is set up on the surface of Planet X. The bob is released from rest and oscillates in a vertical plane. What is the acceleration due to gravity on the surface of Planet ..

Blue line: Jumps alternately between two polar functions of the form:
r = a + bcos(cit + d), where the coefficients a-d are selectable for each function. The angle increment, i, is also selectable. The value of ..

A projectile is launched at an angle from a cliff on an unkown planet. Velocity vectors are shown on the projectile. Use the velocity vectors at two instants of time to determine the acceleration of ..

Three projectiles are launched with different initial velocities and reach the same maximum height. Denote the paths as follow:
A: red
B: green
C: blue
List the projectiles in order of a) increasing initial speed ..

A red ball slides off a table. Ignoring friction, which animation correctly represents the path of the ball? Enter 1, 2, 3, or 4 to change animations. The horizontal and vertical positions, velocities, and accelerations of the ball are ..

A bouncing ball is shown in the animation. What is the ratio of the vertical velocity of the ball just after it hits the ground to the vertical velocity of the ball just before it ..

Two blocks are connected by a massless, unstretchable string which passes over a frictionless, massless pulley. There is no friction between the red block and the plane. When the blue block is released, the system ..

Two blocks are connected by a massless, unstretchable string which passes over a frictionless, massless pulley. There is no friction between the red block and the plane. When the blue block is released, the system ..

Two blocks are connected by a massless, unstretchable string which passes over a frictionless, massless pulley. There is no friction between the red block and the plane. When the blue block is released, the system ..

Two blocks are connected by a massless, unstretchable string which passes over a frictionless, massless pulley. There is no friction between the red block and the plane. When the blue block is released, the system ..

The upper pane shows a pulse moving to the right on a string while the lower pane shows a pulse moving to the left. If the two pulses move in strings of the same linear ..

The upper pane shows a pulse moving to the right on a string while the lower pane shows a pulse moving to the left. If the tension in the two strings is the same, how ..

The upper pane shows a pulse moving to the right on a string while the lower pane shows a pulse moving to the left. If the linear density of the upper string is twice that ..

The red and blue objects have the same mass and oscillate in SHM with the same period and amplitude. The only thing different is the phase. Click Show Graph to see position vs. time graphs ..

A ball oscillates in simple harmonic motion about the origin, while a second ball moves at constant speed in a circular path. Both balls start at y = 0 and have the same initial velocity. The black ..

A ball oscillates horizontally in simple harmonic motion on a frictionless surface. Write the equation of the ball's motion. The grid spacing is 0.01 m. Click Show Graph to see graphs of position and velocity vs. ..

A ball oscillates horizontally in simple harmonic motion on a frictionless surface. The ball is initially moving. Write the equation of the ball's motion. The grid spacing is 0.01 m. Click Show Graph to see graphs ..

When you play the animation, the block oscillates horizontally about the origin on a frictionless table. The origin is in the center, the direction of +x is to the right, and the grid spacing is 0.02 ..

A block slides frictionlessly toward a relaxed spring. As the block compresses the spring, the spring does work on the block, bringing it to a stop. Determine the spring constant of the spring.
Caution: Unphysical ..

A block slides frictionlessly toward a relaxed spring. As the block compresses the spring, the spring does work on the block. A vector representing the spring force is shown as well as a graph of ..

An object moving horizontally is slowed by a force of kinetic friction. Adjust the magnitude of the initial velocity so that the left side of the block stops at the left-hand edge of the screen.

A vertical rod is attached to one end of a string and oscillated at a constant frequency. This produces a transverse wave that travels to the right along the string. The red dots represent selected ..

Each of the numbered diagrams shows three vectors. In each diagram, the blue vector is A, the red vector B, and the green vector C. For which diagrams do two of the vectors add to ..

Play the animation to show a position vs. time graph of a uniformly-accelerating object. The blue line remains tangent to the path of the object. Therefore, the slope of the blue line is the instantaneous ..

The situation is similar to the last problem but with different initial values. Change the inputs in order to model the motion of an object thrown vertically from the ground (initial position of 0 m) at 25 ..

A position vs. time graph of a uniformly-accelerating object is shown. The blue line is always tangent to the path of the object. Determine the acceleration of the object by first finding the velocities at ..